Understanding Electromagnetic Theory: Fundamentals and Applications

1. EKT 241/4:ELECTROMAGNETIC THEORY UNIVERSITI MALAYSIA PERLIS PREPARED BY: NORDIANA MOHAMAD SAAID dianams@unimap.edu.my CHAPTER 1 - INTRODUCTION

2. Electrostatic vs. Magnetostatic UNIVERSITI MALAYSIA PERLIS

3. Timeline for Electromagneticsin the Classical Era • 1785 Charles-Augustin de Coulomb (French) demonstrates that the electrical force between charges is proportional to the inverse of the square of the distance between them. UNIVERSITI MALAYSIA PERLIS

4. Timeline for Electromagneticsin the Classical Era • 1835 Carl Friedrich Gauss (German) formulates Gauss’s law relating the electric flux flowing through an enclosed surface to the enclosed electric charge. UNIVERSITI MALAYSIA PERLIS

5. Timeline for Electromagneticsin the Classical Era • 1873 James Clerk Maxwell (Scottish) publishes his “Treatise on Electricity and Magnetism” in which he unites the discoveries of Coulomb, Oersted, Ampere, Faraday and others into four elegantly constructed mathematical equations, now known as Maxwell’s Equations. UNIVERSITI MALAYSIA PERLIS

6. Units and Dimensions • SI Units • French name ‘Systeme Internationale’ • Based on six fundamental dimensions UNIVERSITI MALAYSIA PERLIS

7. Multiple & Sub-Multiple Prefixes Example: • 4 x 10-12 F becomes 4 pF UNIVERSITI MALAYSIA PERLIS

8. The Nature of Electromagnetism Physical universe is governed by 4 forces: • nuclear force – strongest of the four but its range is limited to submicroscopic systems, such as nuclei • weak-interaction force – strength is only 10-14 that of the nuclear force. Interactions involving certain radioactive particles. • electromagnetic force – exists between all charged particles. The dominant force in microscopic systems such as atoms and molecules. Strength is of the order 10-2 of the nuclear force • gravitational force – weakest of all four forces. Strength is of the order 10-41 that of the nuclear force. Dominant force in macroscopic systems, e.g solar system UNIVERSITI MALAYSIA PERLIS

9. The Electromagnetic Force Where; m2, m1 = masses R12= distanceG = gravitational constant = unit vector from 1 to 2 Gravitational force – between two masses UNIVERSITI MALAYSIA PERLIS

10. Electric fields • Electric fields exist whenever a positive or negative electrical charge is present. • The strength of the electric field is measured in volts per meter (V/m). • The field exists even when there is no current flowing. • E.g rubbing a rubber sphere with a piece of fur.

11. where = radial unit vector pointing away from charge Electric Fields Electric field intensity, E due to charge q UNIVERSITI MALAYSIA PERLIS

12. Electric Fields Coulomb’s law Force between charges q1 and q2 UNIVERSITI MALAYSIA PERLIS Where; Fe21 = electrical force q1,q2 = charges R12 = distance between the two charges = unit vector ε0 = electrical permittivity of free space

13. Electric Fields Electric flux density, D UNIVERSITI MALAYSIA PERLIS where E = electric field intensityε = electric permittivity of the material

14. Magnetic Fields • Magnetic field arise from the motion of electric charges. • Magnetic field strength (or intensity) is measured in amperes per meter (A/m). • Magnetic field only exist when a device is switched on and current flows. • The higher the current, the greater the strength of the magnetic field. UNIVERSITI MALAYSIA PERLIS

15. Magnetic Fields • Magnetic field lines are induced by current flow through coil. • Magnetic field strength or magnetic field intensity is denoted as H, the unit is A/m. UNIVERSITI MALAYSIA PERLIS north pole south pole

16. Magnetic Fields • Velocity of light in free space, c where µ0 = magnetic permeability of free space = 4π x 10-7 H/m • Magnetic flux density, B (unit: Tesla) where H = magnetic field intensity UNIVERSITI MALAYSIA PERLIS

17. Permittivity • Describes how an electric field affects and is affected by a dielectric medium • Relates to the ability of a material to transmit (or “permit”) an electric field. • Each material has a unique value of permittivity. • Permittivity of free space; • Relative permittivity; UNIVERSITI MALAYSIA PERLIS

18. Permeability • The degree of magnetization of a material that responds linearly to an applied magnetic field. • The constant value μ0 is known as the magnetic constant, i.e permeability of free space; • Most materials have permeability of except ferromagnetic materials such as iron, where is larger than . • Relative permeability; UNIVERSITI MALAYSIA PERLIS

19. The Electromagnetic Spectrum UNIVERSITI MALAYSIA PERLIS

20. Electromagnetic Applications UNIVERSITI MALAYSIA PERLIS

21. Review of Complex Numbers • A complex number z is written in the rectangular form Z = x ± jy • x is the real ( Re ) part of Z • y is the imaginary ( Im ) part of Z • Value of • Hence, x =Re (z) , y =Im (z) UNIVERSITI MALAYSIA PERLIS

22. Forms of Complex Numbers • Using Trigonometry, convert from rectangular to polar form, • Alternative polar form, UNIVERSITI MALAYSIA PERLIS

23. Forms of complex numbers • Relations between rectangular and polar representations of complex numbers. UNIVERSITI MALAYSIA PERLIS

24. Forms of complex numbers UNIVERSITI MALAYSIA PERLIS NB: θ in degrees

25. Complex conjugate • Complex conjugate, z* • Opposite sign (+ or -) and with * superscript (asterisk) • Product of a complex number z with its complex conjugate is always a real number. • Important in division of complex number. UNIVERSITI MALAYSIA PERLIS

26. Equality • z1 = z2 if and only if x1=x2 AND y1=y2 • Or equivalently, UNIVERSITI MALAYSIA PERLIS

27. Addition & Subtraction UNIVERSITI MALAYSIA PERLIS

28. Multiplication in Rectangular Form • Given two complex numbers z1 and z2; • Multiplication gives; UNIVERSITI MALAYSIA PERLIS

29. Multiplication in Polar Form • In polar form, UNIVERSITI MALAYSIA PERLIS

30. Division in Rectangular Form • For UNIVERSITI MALAYSIA PERLIS

31. Division in Polar Form UNIVERSITI MALAYSIA PERLIS

32. Powers • For any positive integer n, • And, UNIVERSITI MALAYSIA PERLIS

33. Powers • Useful relations UNIVERSITI MALAYSIA PERLIS